Question: Solve for $x$ and $y$ using elimination. ${6x-6y = -24}$ ${-5x-5y = -60}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $6$ ${30x-30y = -120}$ $-30x-30y = -360$ Add the top and bottom equations together. $-60y = -480$ $\dfrac{-60y}{{-60}} = \dfrac{-480}{{-60}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {6x-6y = -24}\thinspace$ to find $x$ ${6x - 6}{(8)}{= -24}$ $6x-48 = -24$ $6x-48{+48} = -24{+48}$ $6x = 24$ $\dfrac{6x}{{6}} = \dfrac{24}{{6}}$ ${x = 4}$ You can also plug ${y = 8}$ into $\thinspace {-5x-5y = -60}\thinspace$ and get the same answer for $x$ : ${-5x - 5}{(8)}{= -60}$ ${x = 4}$